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Miklós Schweitzer 1986, Problem 7

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September 12, 2016
Miklos Schweitzercollege contestsfunctionSummation

Problem Statement

Prove that the series ∑pcpf(px)\sum_p c_p f(px), where the summation is over all primes, unconditionally converges in L2[0,1]L^2[0,1] for every 11-periodic function ff whose restriction to [0,1][0,1] is in L2[0,1]L^2[0,1] if and only if ∑p∣cp∣<∞\sum_p |c_p|<\infty. (Unconditional convergence means convergence for all rearrangements.) [G. Halasz]
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